System and Method for Mapping Symbols for MIMO Transmission

ABSTRACT

Methods and devices are provided for MIMO OFDM transmitter and receivers having odd and/even numbers of transmit antennas. Various methods for pre-coding information bits before space time coding (STC) are described for enabling transmission of information bits over all antennas. Methods of decoding received signals that have been pre-coded and STC coded are also provided by embodiments of the invention. Pilot patterns for downlink and uplink transmission between a base station and one or more wireless terminals for three transmit antenna transmitters are also provided. Variable rate codes are provided that combine various fixed rate codes in a manner that results in codes whose rates are dependent on all the various fixed rate codes that are combined

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 60/585,583 filed on Jul. 7, 2004 and U.S. ProvisionalPatent Application No. 60/601,178 filed on Aug. 13, 2004, which arehereby incorporated by reference in their entirety.

FIELD OF THE INVENTION

The invention relates to MIMO (multiple input, multiple output)communications systems.

BACKGROUND OF THE INVENTION

Current communication techniques and associated air interfaces forwireless communication networks achieve limited capacity, accessperformance, and throughput. The existing specification of IEEE802.16ehas deficiencies in power balanced space time codes for odd number oftransmit antennas.

Furthermore the existing specification of IEEE802.16e has deficienciesin being able to support users on different layers with sufficientredundancy.

SUMMARY OF THE INVENTION

According to a first aspect of the invention, there is provided a methodfor transmitting on four transmit antennas comprising: pre-codinginformation bits to generate four transmit symbols, encoding two of thetransmit symbols into a first Alamouti matrix and encoding another twoof the transmit symbols into a second Alamouti matrix; transmitting thetwo Alamouti matrices on four antennae over four time intervals or fourfrequencies by: transmitting the first Alamouti matrix on two antennaeand two of the four time intervals or two of the four frequencies;transmitting the second Alamouti matrix on the other two antennae andthe other two of the four time intervals or the other two of the fourfrequencies; wherein the pre-coding and encoding are such that all ofthe information bits are represented in what is transmitted from eachantenna.

According to an embodiment of the first aspect of the invention thepre-coding comprises, generating the four transmit symbols by mapping Minformation bits as two sets of M/2 bits, wherein the first set of M/2bits is mapped on a first and a third 2^((M/2)) QAM mappingconstellation to produce first and third transmit symbols, and thesecond set of M/2 bits is mapped on a second and a fourth 2^((M/2)) QAMmapping constellation to produce second and fourth transmit symbols,wherein the first and second transmit symbols are encoded in the firstAlamouti matrix and the third and fourth transmit symbols are encoded inthe second Alamouti matrix.

According to another embodiment of the first aspect of the invention thethird and fourth mapping constellations are permuted mappings of thefirst second and mapping constellations, respectively.

According to another embodiment of the first aspect of the invention thesecond and fourth mapping constellations are the same as the first andthird mapping constellations, respectively.

According to another embodiment of the first aspect of the invention thepre-coding comprises: mapping four pairs of information bits to 4-PSKsymbols by mapping each pair of bits on a respective one of four rotated4-PSK mapping constellations; generating transmit symbols by formingcombinations of the real and imaginary components of the 4-PSK symbols.

According to another embodiment of the first aspect of the invention themethod comprises forming combinations of the real and imaginarycomponents of the 4-PSK symbols comprises generating the followingtransmit symbols: s₁=Re{C₁}+jRe{C₂}, s₂=Re{C₃}+jRe{C₄},s₃=Im{C₁}+jIm{C₂}, and s₄=Im{C₃}+jIm{C₄}, where C₁ is the first rotated4-PSK mapping constellation, C₂ is the second rotated 4-PSK mappingconstellation, C₃ is the third rotated 4-PSK mapping constellation, andC₄ is the fourth rotated 4-PSK mapping constellation.

According to another embodiment of the first aspect of the inventioneach respective one of four rotated 4 PSK mapping constellations isrotated by an angle π/4−θ where θ=tan⁻¹(⅓).

According to another embodiment of the first aspect of the invention thepre-coding comprises: generating four transmit symbols by mapping Minformation bits as two sets of M/2 bits, wherein the first set of M/2bits is mapped on one layer of a first two layer 2^((M/2)) PSK mappingconstellation and one layer of a second two layer 2^((M/2)) PSK mappingconstellation to produce first and third transmit symbols, and thesecond set of M/2 bits is mapped on the other layer of the first twolayer 2^((M/2)) PSK mapping constellation and the other layer of thesecond two layer 2^((M/2)) PSK mapping constellation to produce secondand fourth transmit symbols, wherein the first and second transmitsymbols are encoded in the first Alamouti matrix and the third andfourth transmit symbols are encoded in the second Alamouti matrix.

According to another embodiment of the first aspect of the invention themethod further comprises using a rotation angle of the rotated 4-PSKmapping constellations to increase a minimum determinant distance of a4×4 matrix containing the first and second Alamouti matrices.

According to another embodiment of the first aspect of the invention therotation angle is π/4−θ where θ=½ tan⁻¹(½).

According to another embodiment of the invention, there is provided afour transmit antenna transmitter for performing the methods of thefirst aspect of the invention.

According to another embodiment of the invention, there is provided adevice for receiving and decoding the transmitted first and secondAlamouti matrices of any one of the methods of the first aspect of theinvention.

According to a second aspect of the invention, there is provided amethod for transmitting on three transmit antennas comprising:pre-coding information bits to generate transmit symbols; encoding thegenerated transmit symbols using a space time/frequency block code inwhich each transmit symbol appears an equal number of times and in sucha manner that each of the three transmit antennas is utilized equally;transmitting the space time/frequency block code over the threeantennae; wherein the pre-coding and encoding are such that all of theinformation bits are represented in what is transmitted from eachantenna.

According to a third aspect of the invention, there is provided a methodfor transmitting on three transmit antennas comprising transmitting anAlamouti matrix on two antennas, time multiplexed with a single transmitsymbol transmitted on a third antenna resulting in a block diagonal codematrix with 2×2 and 1×1 matrices as the diagonal elements.

According to an embodiment of the second aspect of the invention thepre-coding comprises: mapping four pairs of information bits to 4 PSKsymbols by mapping each pair of bits on a respective one of four rotated4 PSK mapping constellations; generating transmit symbols by formingcombinations of the real and imaginary components of the 4 PSK symbols.

According to another embodiment of the second aspect of the inventionforming combinations of the real and imaginary components of the 4 PSKsymbols comprises: generating the following transmit symbolss₁=Re{C₁}+jRe{C₂}, s₂=Re{C₃}+jRe{C₄}, s₃=Im{C₁}+jIm{C₂}, ands₄=Im{C₃}+jIm{C₄}, wherein C₁ is the first rotated 4 PSK mappingconstellation, C₂ is the second rotated 4 PSK mapping constellation, C₃is the third rotated 4 PSK mapping constellation, and C₄ is the fourthrotated 4 PSK mapping constellation.

According to another embodiment of the second aspect of the inventioneach respective one of four rotated 4 PSK mapping constellations isrotated by an angle π/4−θ where θ=tan⁻¹ (⅓).

According to a fourth aspect of the invention, there is provided amethod for transmitting a rate=1 space-time block code for a 2n+1antenna transmitter where n>−1, the method comprising transmitting atleast one code set by: for each pair of consecutive transmissionintervals: on each OFDM sub-carrier of a plurality of OPDM sub-carriers,transmitting a respective Alamouti code block containing two transmitsymbols on a respective pair of antennas such that all sub-carriers areused and only one pair of antennas is active during a given pair ofconsecutive transmission intervals for a given sub-carrier.

According to an embodiment of the fourth aspect of the invention thereare three transmit antennas, and during the pair of consecutivetransmission intervals every third sub-carrier starting at k is activeon a first pair of transmit antennas, every third sub-carrier startingat k+1 is active on a second pair of transmit antennas, and every thirdsub-carrier starting at k+2 is active on a third pair of transmitantennas, where k is an index of a first sub-carrier of the plurality ofOFDM sub-carriers.

According to another embodiment of the fourth aspect of the inventionthe active antennas of the given sub-carrier alternate every pair ofconsecutive transmission intervals.

According to an embodiment of the fourth aspect of the invention the atleast one code set is one or more of a group of code sets consisting of:

Code Set-1 Time t Time (t + T) Antenna 1 S₁ −(s₂) * Antenna 2 S₂ (s₁) *

Code Set-2 Time t Time (t + T) Antenna 2 S₃ −(s₄) * Antenna 3 S₄ (s₃) *

Code Set-3 Time t Time (t + T) Antenna 1 S₆ −(s₅) * Antenna 3 S₅ (s₆) *

According to a fifth aspect of the invention, there is provided a methodfor transmitting a rate=2 space-time block code for a three antennatransmitter, the method comprising transmitting at least one code setby: for each pair of transmission intervals; on each OFDM sub-carrier ofa plurality of OFDM sub-carriers, transmitting one code set containingfour transmit symbols on the three antennas such that all sub-carriersare used and all three antennas are active during a given pair oftransmission intervals for a given sub-carrier.

According to an embodiment of the fifth aspect of the invention themethod comprises transmitting one code set comprises transmitting anorthogonal space time/frequency code block including two transmitsymbols on two transmit antennae and two transmit symbols on a thirdtransmit antenna.

According to another embodiment of the fifth aspect of the invention theat least one code set is one or more of a group of code sets consistingof;

Code Set-1 Time t Time (t + T) Antenna 1 S₁ −(s₂) * Antenna 2 S₂ (s₁) *Antenna 3 S₃ (s₄) *

Code Set-2 Time t Time (t + T) Antenna 1 S₇ (s₈) * Antenna 2 S₅ −(s₆) *Antenna 3 S₆ (s₅) *

Code Set-3 Time t Time (t + T) Antenna 1 S₁₀ (s₉) * Antenna 2 S₁₁(s₁₂) * Antenna 3 S₉ −(s₁₀) *

According to embodiments of the invention some of the methods furthercomprise: receiving feedback pertaining to transmission channels of theantennas; selecting, as a function of the feedback how the antennas areto be used in transmitting the at least one code set.

According to embodiments of the invention some of the methods comprisetransmitting an Alamouti matrix on two antennas determined to be mostcorrelated.

According to embodiments of the invention the feedback is an indicatorof which antennas are most correlated.

According to embodiments of the invention some of the methods comprisetransmitting multiple code sets on a selected set of sub-carriers tointroduce additional diversity gain into the system.

According to a sixth aspect of the invention, there is provided a methodfor generating a space time/frequency code for a multi-antennatransmitter comprising: combining various fixed rate spacetime/frequency codes for a given block length of time intervals orfrequencies in a manner that the combination of various fixed rate spacetime/frequency codes utilize the entire transmission space of the givenblock length for each transmit antenna of the multi-antenna transmitterresulting in a space time/frequency code rate that is a function of eachfixed rate space time/frequency code utilized.

According to an embodiment of the sixth aspect of the invention themethod comprises combining two or more different fixed rate spacetime/frequency codes selected from a group of fixed rate spacetime/frequency codes consisting of; a fixed rate space time/frequencycode comprising one symbol in one block that is capable of beingtransmitted on one antenna; a fixed rate space time/frequency codecomprising two symbols in two blocks that are transmitted on twoantennas; and a fixed rate space time/frequency code comprising threesymbols in two blocks that are transmitted on three antennas.

According to embodiments of the invention, there is provided amulti-antenna transmitter for performing the methods described above.

According to a seventh aspect of the invention, there is provided amethod of transmitting over three transmit antennas comprisings for eachantenna, generating a respective sequence of OFDM symbols, each OFDMsymbol having a plurality of sub-carriers carrying data or pilots, andtransmitting the sequence of OFDM symbols; inserting pilots for thethree antennas collectively in groups of pilots each group containing apilot for each antenna, the groups scattered in time and frequency.

According to an embodiment of the seventh aspect of the invention, eachgroup comprises one sub-carrier by three time intervals.

According to another embodiment of the seventh aspect of the invention,each group comprises one time interval by three sub-carriers.

According to another embodiment of the seventh aspect of the invention,each group comprises a first and a second pilot on a first sub-carrierover two time intervals and a third pilot on an adjacent sub-carrierlocated in the same time interval as one of the first and second OFDMsymbols.

According to another embodiment of the seventh aspect of the invention,each group comprises, in a one sub-carrier by four time intervalsarrangement or a one time interval by four sub-carriers arrangement, onepilots for each antenna in three of the four time intervals or three ofthe four sub-carriers, respectively.

According to another embodiment of the invention there is provided athree transmit antenna transmitter for performing the methods ofembodiments of the invention described above.

According to another embodiment of the invention there is provided adevice for receiving and decoding the transmitted first and secondAlamouti matrices of the methods of embodiments of the inventiondescribed above.

According to another embodiment of the invention there is provided amethod for transmitting on an even number of transmit antennascomprising: pre-coding information bits to generate 2N transmit symbols;encoding each pair of transmit symbols into a respective one of NAlamouti matrices; transmitting the N Alamouti matrices on 2N antennaeover 2N time intervals or 2N frequencies by: transmitting each Alamoutimatrix on two antennas and a respective two of the 2N time intervals ora respective two of the 2N frequencies; wherein the pre-coding andencoding are such that all of the information bits are represented inwhat is transmitted from each antenna.

According to another embodiment of the invention there is provided amethod for transmitting on an odd number of transmit antennascomprising: pre-coding information bits to generate 2N transmit symbols;encoding the 2N transmit symbols using a space time/frequency block codein which each transmit symbol appears an equal number of times and insuch a manner that each of the transmit antennas is utilized equally;transmitting the space time/frequency block code over the transmitantennas; wherein the pre-coding and encoding are such that all of theinformation bits are represented in what is transmitted from eachtransmit antenna.

According to another embodiment of the invention, there is provided afour antenna transmitter comprising: a pre-coder for pre-codinginformation bits to generate four transmit symbols; and a spacetime/frequency block encoder for encoding and transmitting the fourtransmit symbols, wherein the space time/frequency block encoder encodestwo of the transmit symbols into a first Alamouti matrix and encodinganother two of the transmit symbols into a second Alamouti matrix andtransmits the two Alamouti matrices on four antennas over four timeintervals or four frequencies by: transmitting the first Alamouti matrixon two antennas and two of the four time intervals or two of the fourfrequencies; and transmitting the second Alamouti matrix on the othertwo antennas and the other two of the four time intervals or the othertwo of the four frequencies; wherein the pre-coding and encoding aresuch that all of the information bits are represented in what istransmitted from each antenna.

According to another embodiment of the invention, there is provided athree antenna transmitter comprising: a pre-coder for pre-codinginformation bites to generate transmit symbols: and a spacetime/frequency block encoder for encoding and transmitting the generatedtransmit symbols, wherein each transmit symbol appears an equal numberof times and the three transmit antennas are utilized equally.

The three and four antenna transmitters contain hardware and/or softwarefor performing the pre-coding and encoding. In some embodiments of theinvention, the hardware may include an application specific integratedcircuit (ASIC), digital signal processing (DSP) chip, or fieldprogrammable gate array.

Other aspects and features of the present invention will become apparentto those ordinarily skilled in the art upon review of the followingdescription of specific embodiments of the invention in conjunction withthe accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the invention will now be described withreference to the attached drawings in which:

FIG. 1A though FIG. 1E are block diagrams showing an example user tosub-channel and antenna mapping scheme;

FIG. 2 is a schematic diagram for a four antenna transmitter including aknown pre-coding structure;

FIG. 3 is a graphical representation of a constellation mapping utilizedby the transmitter of FIG. 1;

FIG. 4 is a graphical representation of a 16 QAM constellation mappingfor use by embodiments of the invention;

FIG. 5 is a schematic diagram for a four antenna transmitter accordingto an embodiment of the invention;

FIG. 6 is a graphical representation of a constellation constructionaccording to an embodiment of the invention;

FIG. 7 is a graphical representation of a constellation of a transmittedcodeword generated according to an embodiment of the invention;

FIG. 8 is a graphical representation of a pre-coding B PSK two layerconstellation mapping according to another embodiment of the invention;

FIG. 9 is a graphical representation of a pre-coding 16 QAMconstellation mapping according to another embodiment of the invention;

FIG. 10 is an example of a space-time code set sub-carrier mappingpattern for three transmit antennas according to an embodiment of theinvention;

FIG. 11 is a block diagram of a four antenna OFDM transmitter in whichdata and pilot are modulated onto each OFDM signal;

FIG. 12 is a downlink (DL) pilot pattern for a three transmit antennaFUSC (fully used sub-channelization) permutation according to anembodiment of the invention;

FIG. 13 is a DL pilot pattern for a three transmit antenna FUSCpermutation according to another embodiment of the invention;

FIG. 14 is a DL pilot pattern for a three transmit antenna FUSCpermutation according to another embodiment of the invention;

FIG. 15 is a DL pilot pattern for a three transmit antenna FUSCpermutation according to another embodiment of the invention;

FIG. 16 is a DL pilot pattern for a three transmit antenna FUSCpermutation according to another embodiment of the invention;

FIG. 17 is a DL pilot pattern for a three transmit antenna PUSC(partially used sub-channelization) permutation according to anotherembodiment of the invention;

FIG. 18 is a pilot pattern for three transmit antennas in an uplink (UL)STC (space time code) tile format according to an embodiment of theinvention;

FIG. 19 is a pilot pattern for three transmit antennas in an UL STC tileformat according to another embodiment of the invention;

FIG. 20 is a pilot pattern for three transmit antennae in an UL tileformat for optional PUSC zones according to an embodiment of theinvention;

FIG. 21 is a pilot pattern for three transmit antennas in an UL tileformat for optional PUSC zones according to another embodiment of theinvention;

FIG. 22 is a pilot pattern for three transmit antennas in an DL tileformat for optional AMC (adaptive modulation and coding) zones accordingto an embodiment of the invention;

FIG. 23 is a pilot pattern for a three transmit antenna in an UL tileformat for optional AMC zones according to another embodiment of theinvention;

FIG. 24A-24H is a collection of schematic diagrams of variable rate STCcodes for two transmit antennas according to embodiments of theinvention; and

FIG. 25A-25E is a collection of schematic diagrams of variable rate STCcodes for three transmit antennas according to embodiments of theinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

By way of background to more fully understand embodiments of theinvention, a basic Multiple Input Multiple Output—Orthogonal FrequencyDivision Multiple Access (MIMO-OFDMA) air interface is described below,for IEEE802.16e for instance, to enable the joint exploitation of thespatial time frequency and multi-user-diversity dimensions to achievevery high capacity broadband wireless access for both nomadic and mobiledeployments. OFDM transmission may be used for down-link (DL) and/orup-link (UL) transmissions to increase the capacity and quality of theaccess performance. MIMO transmission may be used to increase thenetwork and user throughput, and multi-beam forming transmission may beused to increase aggregated network capacity. A more detaileddescription of an example of a MIMO-OFDMA air interface is found in U.S.patent application Ser. No. <attorney docket number 71493-1330> assignedto the same assignee as the present application and incorporated hereinby reference in its entirety.

By way of overview in a MIMO-OPDM system, each user can be mapped onto adifferent OFDM resource which might be a sub-channel, e.g. an AMC(adaptive modulation and coding) sub-channel and/or a diversitysub-channel. For single Input Single Output (SISO) systems, user mappingis preferably dependent on a channel quality indicator (CQI) only, whilefor the MIMO case, mapping is preferably dependent on the auxiliarymetric channel eigenvalue indicator (CEI) in addition to CQI. For MIMOusers, preferably, multiple different space-time coding schemes aresupported such as SM (spatial multiplexing) and STTD (space-timetransmit diversity).

On a continuous basis, there is a stream of OFDM symbols associated witheach transmit antenna. Bach user may be first mapped onto one ormultiple OFDM symbols and each OFDM symbol may then be mapped onto itsassociated antenna. Such mapping also allows per-antenna rate control(PARC) to be performed in some implementations.

Each OFDM symbol may be mapped onto its associated antenna in thesub-carrier domain. For certain sub-carriers, if no specific user datais mapped, then a null assignment to such sub-carrier may be fed intothe corresponding antenna.

A very simple example of what might be transmitted at a specific instantin time as a result of a particular OFDM symbol and antenna mapping isshown in FIG. 1A. FIG. 1A shows a four antenna transmit system that, inthe instance depicted, is being used to transmit six user packets60,62,64,66,68,70 each of which undergoes FEC (forward error correction)and modulation. A specific mapping of the six packets of six users isshown for a particular time instant. Over time, the number of users,and/or the manner in which the user packets are mapped are preferablydynamically changing.

For the particular time instant, the OFDM bandwidth is allocated in fourdistinct frequency bands F1,F2,F3,F4. These might for example beconsidered AMC (adaptive modulation and coding) sub-channels. A similarapproach can be employed for diversity sub-channels.

Bach packet is to be mapped onto the four antennas using a selectedmapping scheme. In some situations, multiple different schemes areavailable for a given number of transmit antennas and receive antennas.For example, for a 2×2 system, preferably STTD or SM (BLAST) can beselected. In other situations only a single scheme is implemented foreach antenna permutation. Single antenna users use a SISO (which mayinvolve PARC) transmission scheme.

The first packet 60 is transmitted using only antenna 1 on band F3implying a 1×1 SISO transmission.

The second packet 62 is transmitted on both antennas 1 and 2 in band P4implying a 2×1, 2×2 or 2×4 MIMO transmission.

The third packet 64 is transmitted only on antenna 2 in band F3, againimplying a 1×1 SISO transmission.

The fourth packet 66 is transmitted on band F2 over antenna 3.

The fifth packet 68 is transmitted on band F1 on both of antennas 3 and4.

Finally, packet 70 is transmitted on only band F2 of antenna 4.

Generally, each packet can be mapped individually to some or all of theantennas. This enables MIMO and non-MIMO users to be mixed. In the aboveexample, packets 60, 64, 66 and 70 are for non-MIMO users. Packets 62and 64 are for MIMO users.

Please note that the flexible mapping of MIMO and non-MIMO users isapplied both in the context of “partial utilization” and “fullutilization”. With partial utilization, a given base station only hasaccess to part of the overall OFDM band. In this case, the sub-bandsF1,F2,F3,F4 defined for the example of FIG. 1A would fall within thedefined part of the overall band. With partial utilization, differentbase stations that are geographically proximate may be assigneddifferent bands. With full utilization, each base station uses theentire OFDM band. With such an implementation, for the particularexample of FIG. 1A the sub-bands F1,F2,F3,F4 would map to the entireband.

For SISO users, a single band on a single antenna will be used. Asdiscussed, for a MIMO user the configuration is denoted as N_(T)×N_(R).

The flexible structure illustrated by way of example in FIG. 1A can beused for both STTD and BLAST. For example, the packet 62 may betransmitted using the band P4 on antennas 1 and 2 using either BLAST orSTTD.

The particular example shown in FIG. 1A is designed to show theco-existence of SISO and MIMO be it STTD and/or BLAST. Of course thenumber of sub-bands, and their shape, size, location, etc., within theOFDM band are implementation specific details. The mapping can be doneon a per OFDM symbol basis, or for multiple OFDM symbols.

Another way to think of this is that each time-frequency block that isdefined can have its own matrix. Once the matrix is specified, thenumber of antennas at the output is defined. For example, a 2×2 matrixrequires two antennas a 4×4 matrix requires four antennas. The matrixalso determines, not necessarily uniquely, the number of different usersthat can be mapped. Particular examples are given in the tables below.

The content for multiple users of course needs to be mapped in a mannerthat is consistent and non-conflicting. Also, each user needs to beinformed of where/when its content will be transmitted. Details of amethod of performing this signalling are defined in applicants'co-pending application no. <attorney docket 71493-1329 entitled Methodsfor Supporting MIMO Transmission in OFDM Applications> herebyincorporated by reference in its entirety.

For each individual user, the antenna mapping enables STTD, SM and PARCtransmissions for either the AMC sub-channel or the diversitysub-channel. Any one of six different mapping configurations can beapplied to each individual user, including three 4-transmit antennamappings, 2-transmit antenna mappings and a single antenna mapping.

The uplink may include, for example, two modes: (1) STTD for dualtransmit antenna capable wireless terminals and (2) Virtual-MIMO forsingle transmit antenna capable wireless terminals.

Referring now to FIGS. 1B,1C,1D and 1R shown are specific transmitterconfigurations. The transmitter may be dynamically reconfigurable toenable transmission to multiple users using respective transmissionformats. The particular examples of FIGS. 1B,1C,1D, and 1E below can beconsidered “snapshots” of such a reconfigurable transmitter. Theseconfigurations can also exist simultaneously for different sub-bands ofan overall OFDM band that is being employed. For example, theconfiguration of FIG. 1B might be used for a first set of sub-channelsor a first OFDM band and associated user(s); the configuration of FIG.1C might be used for a second set of sub-channels or a second OFDM bandand associated user(s) and so on. Of course, many of the components thatare shown as being replicated would not need to be physicallyreplicated. For example, a single IFFT and associated transmit circuitrycan be used per antenna with the different mappings being performed andthen input to appropriate sub-carriers of the IFFT.

FIG. 1B shows an example configuration with a matrix that performs STTDencoding based on a single input stream, and with horizontal encodingfor two, three or four transmit antennas. In a transmitter structure,generally indicated at 1001, an input stream 1000 is encoded, alsoreferred to as pre-coded, and modulated and then STC encoded in spacetime encoder 1002 having two, three or four outputs that are then fed torespective transmit chains and transmitted. A corresponding receiverstructure is indicated generally at 1004.

FIG. 1C shows an example configuration with a matrix that performs STTDencoding for multiple input streams, and with horizontal encoding fortwo, three or four transmit antennas. Input streams 1006,1008 (only twoshown, more possible) are encoded and modulated and then STC encoded inspace time encoder 1010 having two, three or four outputs that are thenfed to respective transmit chains and transmitted. STTD matrices areexamples of matrices that may be employed; other matrices are possible.

FIG. 1D shows an example configuration with a matrix that performs SM(e.g. BLAST) encoding for a single input stream. Input stream 1012 isencoded and modulated and than demultiplexed into two, three or fourstreams 1012,1014 that are fed to respective transmit chains andtransmitted. SM matrices are examples of matrices that may be employed;other matrices are possible. This is an example of so-called “verticalencoding” where the input symbols of a given input stream are verticallydistributed (i.e. simultaneous in time) between the multiple antennas.

FIG. 1E shows an example configuration with a matrix that performs SM(e.g. BLAST) encoding for multiple input streams. Input streams 1020,1022 (only two shown, more possible) are encoded and modulated fed torespective transmit chains and transmitted. SM matrices are examples ofmatrices that may be employed; other matrices are possible. This is anexample of so-called “horizontal encoding” where the input symbols of agiven input stream are horizontally distributed (i.e. sequentially intime) on a single antenna.

Pre-Coding for Four Transmit Antennas

Rate=1 space time block codes (STBC) or space frequency block codes(SFBC) for four transmit antennas, examples of which are more fullydisclosed in U.S. patent application Ser. No. <attorney docket No.71493-1327> assigned to the assignee of the present application, providea diversity order of one per transmit symbol, while achieving fulldiversity with the help of FEC codes. A diversity order equal to onemeans that in four time intervals, four transmit symbol are transmitted.An example of such a rate=1 STBC code is presented below in which two2×2 Alamouti code blocks are located on the diagonal of the STBC code.

$\quad\begin{bmatrix}s_{1} & s_{2} & 0 & 0 \\{- s_{2}^{*}} & s_{1}^{*} & 0 & 0 \\0 & 0 & s_{3} & s_{4} \\0 & 0 & {- s_{4}^{*}} & s_{3}^{*}\end{bmatrix}$

The code matrix for the Alamouti code is presented below.

Time t Time (t + T) Antenna 1 s₁ s₂ Antenna 2 −s₂* s₁*

The Alamouti code has several properties, which makes it perfect forspace diversity. The signals are orthogonal; hence full diversity isachieved at the receiver side. The transmit power is balanced betweenthe two antennas (and the two time slots); hence a low cost poweramplifier can be used, which in turn reduces the modem cost. Its coderate is 1; hence no throughput is sacrificed. Its maximum likelihooddecoder is very simple, which makes the cost of an optimal decodernegligible.

This is only one example of an STBC code using Alamouti codes. FurtherSTBC codes with different arrangements of transmit symbols are describedin U.S. patent application Ser. No. <attorney docket No. 71493-1327>which is hereby incorporated by reference in its entirety.

A known pre-coding technique identified below can be used in generatingthe transmit symbols [s₁,s₂,s₃,s₄] by multiplying a pre-coding symbolmatrix with a vector of information symbols [C₁,C₂,C₃,C₄].

$\begin{bmatrix}s_{1} \\s_{2} \\s_{3} \\s_{4}\end{bmatrix} = {{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & \alpha_{0} & 0 & 0 \\0 & 0 & 1 & \alpha_{1} \\1 & \alpha_{2} & 0 & 0 \\0 & 0 & 1 & \alpha_{3}\end{bmatrix}}\begin{bmatrix}C_{1} \\C_{2} \\C_{3} \\C_{4}\end{bmatrix}}$

The vector [C₁,C₂,C₃,C₄] includes information symbols for rate=2 QPSK(quadrature phase shift keying). The information symbols for example mayeach represent a pair of bits. The pre-coding symbol matrix is oneexample of such a matrix used in a pre-coding operation.

In an optimal pre-coding symbol matrix the parameters are governed bythe relationships |α₀−α₂|=π and |α₁−α₃|=π where α₀=e^(jπ/4),α₁=e^(jπ5/4).

FIG. 2 illustrates an example of a four antenna transmitter, generallyindicated at 100, including a constellation mapping component 110 and aSTBC coding component 120. Transmission data bits b₀ and b₁ are includedin information symbol C₁, transmission data bits b_(a) and b₃ areincluded in information symbol C₃, transmission data bits b₄ and b₅ areincluded in information symbol C₂, and transmission data bits b₆ and b₇are included in information symbol C₄. The pre-coding operationdescribed above results in s₁ being dependent upon C₁ and C₃ and s₃being dependent upon C₁ and C₃. Symbol s₃ is a permutation of symbol s₁due to the relationship of α₀ and α₂, as noted above. Similarly, symbols₂ and symbol s₄, are dependent on both C₂ and C₄.

FIG. 3 is a 16 QAM constellation map for mapping a 4 bit symbol. Withrespect to the above known pre-coding symbol matrix, for α₀=α₂, theminimum distance between symbols on an inner radius of symbols is d₁ asshown in FIG. 3. The minimum distance between symbols in the outerradius is equal to d₂. For α₀=α₂e^(jπ), the minimum distance betweensymbols is √{square root over (d₁d₂)}. Furthermore, when α₀=α₂e^(jπ) thesymbols on the inner and outer radii are interchanged.

As an alternative to known methods of sending independent QPSK symbolsfor transmit symbols s₁ and s₃ (as well as s₂ and s₄) in the STCB code,an embodiment of the invention includes encoding, or pre-coding, twosets of four bits in such a manner than they are inter-dependent. Afirst set of four bits are mapped onto two different 16 QAM (quadratureamplitude modulation) constellation mappings, S₁ and S₃ as shown in FIG.4, which result in the generation of two transmit symbols, s₁ and s₃.Transmit symbols s₁ and s₃ each contain the first set of four bits, butmapped differently. Similarly, transmit symbols s₂ and s₄ are generatedby pre-coding a second set of four bits on two 16 QAM constellationmappings, for example s₂ and s₄. The 16 QAM constellation mapping is aspecific example mapping. More generally, sets of i bits are mapped toM-ary QAM constellation mappings where M=2^(i), i>2.

The four transmit symbols s₁, s₂, s₃ and s₄ are then STBC coded fortransmission on a four antenna transmitter, for example as follows:

$\quad{\begin{bmatrix}s_{1} & s_{2} & 0 & 0 \\{- s_{2}^{*}} & s_{1}^{*} & 0 & 0 \\0 & 0 & s_{3} & s_{4} \\0 & 0 & {- s_{4}^{*}} & s_{3}^{*}\end{bmatrix},}$

The STBC code rows include symbols to be transmitted by a particulartransmit antenna and the STBC code columns include symbols to betransmitted in time or frequency. Since the generated transmit symbolss₁ and s₃ each represent the same four information bits mapped using twodifferent constellation mappings s₁ and S₃ and the generated symbols s₁and s₃ are transmitted on pairs of antennas 1 and 2, and 3 and 4,respectfully then the four information bits are transmitted over allfour antennas. The same process occurs for the second four informationbits. The fact that all bits are transmitted over all four antennasprovides additional diversity to the system.

In some embodiments the constellation mapping used for S₃ is apermutation, essentially a relabeling, of S₁. The same bits used to mapto transmit symbol s₁ are used to map to symbol s₃ using a differentpermuted constellation. An example set of permuted constellationmappings for S₁ and S₃ are shown in FIG. 4. The 16 QAM constellation forS₁ shows an x-axis labelled as S_(1X) and a y-axis labelled as S_(1Y).The x-axis has coordinate values 11,01,10,00 from the “negative” side tothe “positive” side of the axis. The y-axis has coordinate values11,01,10,00 from the “negative” side to the “positive” side of the axis.These coordinate values represent two 4 PAM (pulse amplitudemodulation). Using these x and y-axis coordinates values, the four bitinformation symbol values are mapped where the first two bits are thex-axis coordinate values and the second two bits are the y-axiscoordinate values. For example, a symbol mapped to S₁ is S_(1X)×S_(1Y).Similar axis labelling is used for S₃, and a symbol mapped to S₃ isS_(3X)×S_(3Y). In some embodiments, S_(1X) and S_(3X) are dependent andS_(1Y) and S_(3Y) are dependent based on the permutation describedabove. A similar constellation is shown for Sa, except that the x-axishas coordinate values 10,11,00,01 from the “negative” side to the“positive” side of the axis. The y-axis has coordinate values10,11,00,01 from the “negative” side to the “positive” side of the axis.It can be seen that the value in the first coordinate value of S_(1X) isthe value in the second coordinate value of S_(3X), the value in thesecond coordinate value of S_(1X) is the value in the fourth coordinatevalue of S_(3X), the value in the third coordinate value of S_(1X) isthe value in the first coordinate value of S_(3X), and the value in thefourth coordinate value of S_(1X) is the value in the third coordinatevalue of S_(3X). It is in this way that S₃ is a different permutedconstellation of s as described above. It is to be understood that thisis one example of such a permutation and that other types of permutationare to be considered within the scope of the invention.

Therefore, a method for pre-coding information and transmitting thegenerated transmit symbols includes a first step of grouping eightinformation bits into two sets of four bits, using the first set of fourbite to address constellation S₁ in FIG. 4 and to address constellationS₃ in FIG. 4 to produce transmit s₁ and s₃ respectively. Similarly,using the second set of four bits to address constellation S₁ in FIG. 4and to address constellation S₃ to produce transmit symbols s₂ and s₄,respectively. More generally, a different pair of constellations may beused to generate transmit symbols s₂ and s₄. In a second step, theresulting transmit symbols are encoded with a desired STBC or SFBC codeand transmitted on the four antennas.

More generally, the pre-coding method can be applied to any even numberof antennas by pre-coding information bits to generate 2N transmitsymbols; encoding each pair of transmit symbols into a respective one ofN Alamouti matrices; transmitting the N Alamouti matrices on 2N antennasover 2N time intervals or 2N frequencies by: transmitting each Alamoutimatrix on two antennas and a respective two of the 2N time intervals ora respective two of the 2N frequencies; wherein the pre-coding andencoding are such that all of the information bite are represented inwhat is transmitted from each antenna.

For example, two sets of bits are each mapped to three different M-aryQAM mapping constellations to generate a total of six transmit symbols.The six transmit symbols are encodes using three Alamouti codes, in asimilar way that four transmit symbols are encoded on two Alamouti codesas described above. As each of the two sets of bits are represented inall three Alamouti matrices, all of the information bits are representedin what is transmitted from each antenna.

FIG. 5 illustrates an example of a four antenna transmitter, generallyindicated at 500, including a constellation mapping component 510 and aSTBC coding component 520 for implementing embodiments of the invention.Two sets of four information data bits, b₀b₁b₂b₃ and b₄b₅b₆b₇ are inputto the constellation mapping component 510. As described above the firstset of four information bits are mapped to constellation S₁ in FIG. 4and mapped to constellation S₃ in FIG. 4 to produce transmit symbols s₁and s₃ respectively. With the second group of four information bitsb₄b₅b₆b₇, similar mappings are done to generate transmit symbols s₂ ands₄. The respective values output from the constellation mappingcomponent 510 for transmit symbols s₁, s₂, s₃ and s₄ are input to theSTBC coding component 520, where the transmit symbols are arranged inthe desired STBC code or SFBC code described above.

FIG. 6 illustrates an intermediate mapping generated by combining thereal components of the mappings to S₁ and S₃. The intermediate mappingof FIG. 6 has an x-axis that corresponds to the x-axis of S₁, S_(1X),and a y-axis that corresponds to the x-axis of S₃, S_(3X). The foursymbols in the intermediate mapping are the coordinates of equal two bitvalues of S_(1X) and S_(3X), that is for example for S_(1X)=00 andS_(3X)=00. Similar intermediate mappings are provided for S_(1Y) andS_(3Y), S_(2X) and S_(4X), and S_(2Y) and S_(4Y). In some embodiments ofthe invention the four intermediate mappings can be used in pre-codingto provide that all information bite are spread over all four transmitantennas. For example, eight information bits are provided forpre-coding in four sets of two bits. Each set of two bite is supplied toone of the four intermediate mappings described above. The transmitsymbols are then generated by combining the real and imaginarycomponents of the four intermediate mappings. Assuming the fourintermediate mappings are defined as C₁-S_(1X)×S_(3X), C₂-S_(1Y)×S_(3Y),C₃=S_(2X)×S_(4X) and C₄=S_(2Y)×S_(4Y), an example of the resultingtransmit symbols is s₁=Re{C₁}+jRe{C₂}, s₂Re{C₃}+jRe{C₄},s₃=Im{C₁}+jIm{C₂}, and s₄=Im{C₃}+jIm{C₄}. In this case all four sets oftwo information bits are represented on all four antennas providingadditional diversity.

FIG. 7 illustrates another example of a four antenna transmitter,generally indicated at 700, including a constellation mapping component710 and a coding component 720. The constellation mapping component 710utilizes four intermediate mappings described above and contains logicto combine the real and imaginary aspects of the mapped symbols togenerate the transmit symbols. Transmission data bite b₀ and b₁ are usedto map on intermediate mapping C₁, transmission data bits b₂ and b₃ areused to map on intermediate mapping C₂, transmission data bits b₄ and b₅are used to map on intermediate mapping C₃, and transmission data bitsb₆ and b₇ are used to map on intermediate mapping C₄. The respectivereal and imaginary components of information symbols C₁ and C₂ are usedto generate transmit symbols s₁ and s₃ and the respective real andimaginary components of information symbols C₃ and C₄ are used togenerate transmit symbols s₂ and s₄. The transmit symbols s₁, s₂, s₃ ands₄ are then supplied to STBC coding component 720 to be assigned to thedesired STBC code or SFBC code, an example of which is shown in FIG. 7.

Decoding

In a preferred implementation of the pre-coding method, Re{s₁} is onlyrelated to Re{s₃} and Im{s₁} is only related to Im{s₃}. In an examplemethod of decoding, Alamouti decoding is performed first to find thescaled estimated symbols {{tilde over (s)}₁,{tilde over (s)}₂,{tildeover (s)}₃,{tilde over (s)}₄};

${\overset{\sim}{s}}_{1} = {\frac{\left( {{h_{1}^{*}r_{1}} + {h_{2}r_{2}^{*}}} \right)}{\delta_{12}^{2}} = {s_{1} + \frac{\left( {{h_{1}^{*}n_{1}} + {h_{2}n_{2}^{*}}} \right)}{\delta_{12}^{2}}}}$

where h₁ and h₂ are channel parameters, n₁ and n₂ are noise parameters,and δ² ₁₂=|h₁|²+|h₂|². Now, we consider Re{{tilde over (s)}₁}+JRe{{tildeover (s)}₃} to find the maximum likelihood estimates of Re{S₁} andRe{S₃}. Typically the noise power in the two dimensions are equal.Therefore, the minimum Euclidean distance between {{tilde over(s)}₁}+jRe{{tilde over (s)}₃} and δ₁₂Re{S₁}+jδ₃₄Im{S₃} can be found,which is a search over four different points.

Table 1 includes the number of computational operations performed ateach defined step for decoding a received signal that has been pre-codedwith the inventive pre-coding method and STBC coded such as would betransmitted from transmitter of the type of FIG. 5 as compared to thenumber of computational operations performed at each defined step fordecoding a received signal that is pre-coded and STBC coded by thetransmitter of FIG. 2. The column entitled “IEEE802.16d” is provided toindicate the number of operations used to decode an Alamouti matrix foreach STTD block that has not been pre-coded according to the IEEE802.16dstandard. One real multiplication operation is equal to one real add,which is represented by A, one complex multiplication operation is equalto four real multiplication operations and two real add operations for atotal of six real adds, which is represented by M, one complex addoperation is equal to 2 real adds, which is represented by m, and a realadd is represented by a. Each “computation” and “LUT” (Look-Up Table)operation is respectively the computational equivalent operation of onereal add. The inventive pre-coding method uses less computational powerto decode the received pre-coded and STBC coded signal than for theother types of coded signals as it is less complex.

TABLE 1 Computational Complexity Analysis Coding using Coding usingTransmitter Transmitter IEEE802.16d of FIG. 2 of FIG. 5 Step- Alamouti 4(2M + A + 2m) 4 (2M + A + 2m) 4 (2M + A + 2m) 1 decoding for each STTDblock Step- Compute the 0 2 × 16 × (2 (1M + 1A) + 1a) 4 × 4 × (2 (1m +1a) + 1a) 2 weighted distance over all 16 constellation points Step-Find the 0 2 × 16 comp 4 × 4 comp 3 maximum distance Step- Generate 4 02 × 4 × 8 LUT 4 × 2 × 2 LUT 4 bit LLR Total Step-1, Step-2 8M + 4A + 8m72M + 68A + 8m + 8M + 4A + 40m + 48a + Step-3 32a + 32comp + 64LUT16comp + 16LUT and Step-4 Total 64 674 176 Ratio 1 10.5 2.7

Optimized Rotation

In the inventive code, Re{s₁}+jRe{S₃} as represented in the mappingconstellation of FIG. 6 (similarly, Re{S₂}+jRe{S₄}, Im{S₁}+jIm{S₃} andIm{S₂}+jIm{S₄}), can be considered as a symbol of a 4 PSK (pulse shiftkeying) constellation mapping rotated by an angle π/4−θ whereθ=tan⁻¹(⅓). The angle of rotation can be optimized to increase theminimum determinant distance of the code. In a preferred embodiment foran optimized rotation:

4 sin θ cos θ=(cos θ−sin θ(cos θ+sin θ)

θ=½ tan⁻¹(½).

Changing the rotation angle does not affect the complexity of decodingand encoding.

Optimizing the angle of rotation applies to pre-coding for use with fourtransmit antennas described above as well as to pre-coding for use withthree transmit antennas described below.

TABLE 2 Performance Analysis Minimum determinant distance Coding usingTransmitter 0.414 of FIG. 2 Coding using Transmitter 0.4 of FIG. 5 (QAM)Coding using Transmitter 0.447 of FIG. 5 (optimized rotation)IEEE2.02.16d 0

In another embodiment of four transmit antenna pre-coding, instead ofsending independent QPSK signals for symbols s₁ and s₃ (as well assymbols s₂ and s₄), dependant two-layer 8PSK signals are transmitted. Insome embodiments, the mapping constellation for the two-layer 8PSKsignal generating symbol s₃ is a permutation (relabeling) of the mappingconstellation for the two-layer 8PSK signal generating symbol s₁.

FIG. 8 shows an example of pre-coding mapping constellations for arate=1, four transmit antenna in which a first mapping constellation isused for generating s₁ and s₁ and a second mapping constellation is usedfor generating s₃ and s₄. In another embodiment of the invention, themapping constellations of FIG. 8 could be used in the mappingconstellation component 510 of the transmitter of FIG. 5 instead of themapping constellations of FIG. 4. In the embodiment for FIG. 8 theradius of the outer layer is 1.3 and the radius of the inner layer is0.55. In some embodiments, the radii of the outer and the inner layersmay vary, but the ratio of the outer layer to the inner layer ismaintained at 1.3:0.55.

Three Antenna Codes

Methods and systems are provided in which each antenna of a MIMOtransmitter with an odd numbers of transmit antennas has equalopportunity to transmit signals. In some embodiments of the inventionfull spatial diversity is achieved within a transmitted code block. Insome embodiments of the invention transmission power of the multipleantennas is balanced.

In known MIMO transmitters with an odd number of transmit antennas, oneof the antennas typically has twice an opportunity to transmit signalsthan the other two antennas. This results in the transmission powerbeing unbalanced within the transmitted code block. Therefore, onlypartial space diversity is achieved due to overweighting of the transmitantenna having twice the opportunity to transmit signals.

Embodiments of the invention presented for the four transmit antennacase can be modified to the case of three transmit antennas by applyingan Alamouti construction to the first two antennas, time multiplexedwith the third antenna resulting in a block diagonal code matrix with2×2 and 1×1 matrices as the diagonal elements.

Let us refer to the two signals obtained by the Alamouti constructionover the first two antennas as S1 and S2 and the signal transmitted overthe third antenna as S3. Note that S1 and S2 have a diversity order oftwo and can be easily decoded using the orthogonality of the Alamoutistructure. The final code is constructed by using a rotatedconstellation, similar to that of FIG. 6, over S1 and one dimension ofS3 (a 3 dimensional constellation with diversity order 3) and a secondsimilar constellation over S2 and the second dimension of S3. The two3-dimensional constellations are encoded/decoded separately. Therotation angle is optimized for the best performance with low decodingcomplexity.

Rate=1, Three Transmit Antenna Pre-Coding

In some embodiments of the invention, a rate=1, three transmit antennapre-coding operation is provided in which an M-ary QAM constellation isused for the pre-coding. For example, for high data rates, 64 QAM issuggested, however similar pre-coding operations can be applied for QAMwith different number of symbols.

In the case of M-ary QAM, half of the constellation symbols have evenparity and half have odd parity. FIG. 9 shows an example of a 16 QAMconstellation, in which symbols designated with a circle have evenparity and symbols designated with a star have odd parity.

An example of a method for pre-coding and transmitting symbols for arate=1 code with three transmit antennas and using a 64 QAMconstellation mapping for the pre-coding operation involves 1) addingone parity bit (e.g. even-parity) to 17 bits of data, 2) determiningthree transmit symbols z1, z2 and z3 from the 64 QAM constellation usingthe total of 18 bits of coded data, and 3) encoding the transmit symbolswith a STBC code, such as

$\begin{bmatrix}z_{1} & {- z_{2}^{*}} & {- z_{3}^{*}} & 0 \\z_{2} & z_{1}^{*} & 0 & z_{3}^{*} \\z_{3} & 0 & z_{1}^{*} & {- z_{2}^{*}}\end{bmatrix},$

where each transmit symbol appears an equal number of times, andantennas are equally utilized. The above STBC code is only one exampleof an STBC code that could be used, other STBC codes are possible.

More generally, a method for pre-coding and transmitting symbols withthree transmit antennas and using an 2^(M) QAM constellation mapping forthe pre-coding operation involves 1) adding one parity bit to 3M−1 bitsof data, 2) determining three transmit symbols z1, z2 and z3 from the2^(M) QAM constellation using the total of 3M bits of coded data, and 3)encoding the transmit symbols with a STBC code

It is to be understood that even though the above example describesspace-time block codes, embodiments of the invention also includespace-frequency block codes.

Rate=1, 3-Transmit Antenna Pre-Coding Decoding

An embodiment of the invention provides for decoding a received signalencoded with the above described pre-coding operation. A first step ofdecoding the space-time code is:

$\hat{z} = {\begin{bmatrix}{\hat{z}}_{1} \\{\hat{z}}_{2} \\{\hat{z}}_{3}\end{bmatrix} = {\frac{1}{{h_{1}}^{2} + {h_{2}}^{2} + {h_{3}}^{2}} \times \hat{H} \times \begin{bmatrix}y_{1} \\y_{2}^{*} \\y_{3}^{*} \\y_{4}^{*}\end{bmatrix}}}$

where, h_(i), i=1 to 3 are channel parameters for each respectivetransmit antenna channel,

$\hat{H} = \begin{bmatrix}h_{1}^{*} & h_{2} & h_{3} & 0 \\h_{2}^{*} & {- h_{1}} & 0 & {- h_{3}} \\h_{3}^{*} & 0 & {- h_{1}} & h_{2}\end{bmatrix}$

is a channel parameter matrix corresponding to the STBC code above, andy_(i), i=1 to 4 represent the originally transmitted symbols.

A second step is, for each complex value {circumflex over (z)}₁,determining the closest point z₁ ^(o) among constellation symbols withodd parity and the closest point z₁ ^(o) among constellation symbolswith even parity.

A third step is selecting the beet choice in terms of minimum distancefrom i among the following options:

Choice one: [z₁ ^(o) z₂ ^(o) z₃ ^(o)];Choice two: [z₁ ^(o) z₂ ^(o) z₃ ^(o)];Choice three: [z₁ ^(o) z₂ ^(o) z₃ ^(o)];Choice fours [z₁ ^(o) z₂ ^(o) z₃ ^(o)].

The second and third steps can be simplified by using a Wagner RuleDecoding method. For instance, in the second step for i=1, 2, 3,determine {tilde over (z)}₁, the closet points from constellation pointsto {circumflex over (z)}₁. If the total parity of the labels for {tildeover (z)}₁, {tilde over (z)}₂, and {tilde over (z)}₃ satisfies the evenparity condition, the decoding is complete, else go to the third step.In the third step, by replacing one of the symbols {tilde over (z)}₁,i=1, 2, 3 with a symbol from a complementary subset of constellationsymbols which has different parity, the parity condition will besatisfied. To do that, a less reliable symbol is determined from {tildeover (z)}₁, i=1, 2, 3 and replaced with the closest symbol from thecomplementary subset of constellation symbols.

Space Time Code Mapping for Three Antenna Transmitter

Tables 3 to 5 provide an example of a rate=1 STBC code for threetransmit antenna transmission. Generally, in the examples, there is onelayer of transmission, since on average, one symbol is transmitted persub-carrier per time instance.

TABLE 3 Code Set-1, Sub-carrier k + 0, Rate = 1, 3 Transmit AntennaeTime t Time (t + T) Antenna 1 S₁ −(s₂) * Antenna 2 S₂ (s₁) *

TABLE 4 Code Set-2, Sub-carrier k + 1, Rate = 1, 3 Transmit AntennasTime t Time (t + T) Antenna 2 S₃ −(s₄) * Antenna 3 S₄ (s₃) *

TABLE 5 Code Set-3, Sub-carrier k + 2, Rate = 1, 3 Transmit Antenna Timet Time (t + T) Antenna 1 S₆ −(s₅) * Antenna 3 S₅ (s₆) *

Tables 6 to 8 provide an example of a rate=2 STBC code for threetransmit antenna transmission. This is a two layer example in whichorthogonal STTD encoding is used for one layer (for example S₁ and S₂ inCode Set-1, S₅ and S₆ in Code Set-2, and S₉ and S₁₀ in Code Set-3) andno such code is used for the other layer (S₃ and s₄ in Code Set-1, S₇and S₆ in Code Set-2, and S₁₁ and S₁₂ in Code Set-3), symbols in thislayer making non-orthogonal contributions.

TABLE 6 Code Set-1, Sub-carrier k + 0, Rate = 2, 3 Transmit AntennasTime t Time (t + T) Antenna 1 S₁ −(s₂) * Antenna 2 S₂ (s₁) * Antenna 3S₃ (s₄) *

TABLE 7 Code Set-2, Sub-carrier k + 1, Rate = 2, 3 Transmit AntennasTime t Time (t + T) Antenna 1 S₇ (s₈) * Antenna 2 S₅ −(s₆) * Antenna 3S₆ (s₅) *

TABLE 8 Code Set-3, Sub-carrier k + 2, Rate = 2, 3 Transmit AntennaeTime t Time (t + T) Antenna 1 S₁₀ (s₉) * Antenna 2 S₁₁ (s₁₂) * Antenna 3S₉ −(s₁₀) *

Additional diversity is provided by having three different code sets.

In the examples above there are three different code sets. Moregenerally, the number of code sets is limited by the number of differentpossible antenna combinations for transmitting symbols.

Tables 3 to 5 are examples for three transmit antennas, more generallyhowever, a method for transmitting a rate=1 space-time block code for a2n+1 antenna transmitter where n>=1, the method comprising transmittingat least one code set by: for each pair of consecutive transmissionintervals: on each OPDM sub-carrier of a plurality of OFDM sub-carriers,transmitting a respective Alamouti code block containing two transmitsymbols on a respective pair of antennas such that all sub-carriers areused and only one pair of antennas is active during a given pair ofconsecutive transmission intervals for a given sub-carrier. Similarly,for Tables 6-8, a method for transmitting a rate=2 space-time block codefor a three antenna transmitter, the method comprising transmitting atleast one code set by; for each pair of transmission intervals: on eachOFDM sub-carrier of a plurality of OFDM sub-carriers, transmitting onecode set containing four transmit symbols on the three antennas suchthat all sub-carriers are used and all three antennas are active duringa given pair of transmission intervals for a given sub-carrier.

In some embodiments, the active antennas of a given sub-carrieralternate every pair of consecutive transmission intervals.

A space time code sub-carrier mapping for three transmit antennas willnow be described with respect to FIG. 10. This example demonstrates howthree code sets can be transmitted, such as those of Tables 3-5. In FIG.10, Code Set-1, Code Set-2, and Code Set-3 are each comprised of twotransmit symbols, where a first transmit symbol is transmitted at afirst time interval t and a second transmit symbol is transmitted at asecond time interval t+T. Code Set-1 is transmitted on a firstsub-carrier k+0, Code Set-2 is transmitted on a second sub-carrier k+l,and Code Set-3 is transmitted on a third sub-carrier k+2. The code setscan be transmitted on multiple available sub-carriers in a sub-carrierband allocated for sub-carrier transmission. The code sets can betransmitted at subsequent periods in time with the same sub-carrierallocation or the respective code sets may be allocated to differentsub-carriers.

While the examples of the code sets above are coded in the timedirection in adjacent time intervals on different sub-carriers, it is tobe understood that the code sets could be coded in the frequencydirection in sub-carriers, adjacent or not, in different time intervals.

Code Set Selection

In some embodiments of the invention, a code set includes an orthogonalSTTD layer and a non-orthogonal layer as described with respect to Table6-8 above. Within the orthogonal STTD layer no inter-symbol interferenceexists. However, interference may exist between the symbols of theorthogonal STTD layer and the symbols of the non-orthogonal layer. If achannel of an uncoded layer is correlated with the channel of a codedlayer, system performance degrades.

In some embodiments, for a closed loop system including a base stationand at least one wireless terminal, two of the most correlated channelsare used for STTD transmission to reduce the possibility of a channel ofan uncoded layer being correlated with the channel of the orthogonalSTTD coded layer. The wireless terminal feeds back a selection of twoantennas to be used for the STTD layer. For example, a particular one ofthe code sets of Tables 6-8 can be selected for a set of sub-carriers ofa given user. In other embodiments, for an open loop system including abase station and at least one wireless terminal, all three code sets areused on different sub-carriers to introduce additional diversity gaininto the system.

Decoding Method for Rate=2, STTD with 3 Transmit Antennae

In some embodiments of the invention a zero-forcing (ZF) algorithm isused for rate=2 STTD decoding, for example decoding the code sets ofTables 6 to 8.

Since one layer is STTD encoded, the performance of the ZF algorithm iscloser to the performance of a maximum likelihood (ML) algorithm thanthe performance of the ZF algorithm as compared to the performance ofthe ML algorithm in the case of BLAST. In some embodiments, softdemapping is weighted in a similar way as in the case of BLAST. In someembodiments, the weighting factors, such as in the case of SNR basedweighting, for STTD coded symbols are the same.

The following equation illustrates a matrix representation of a receivedsignal for an example STTD encoded rate=2 code, for example Code Set-1of Table 6. The received signal can be represented in a matrix format asbeing equal to the channel characteristic matrix multiplied by theoriginally transmitted symbols plus noise:

$\begin{bmatrix}r_{1,1} \\r_{1,2} \\r_{2,1}^{*} \\r_{2,2}^{*}\end{bmatrix} = {{\begin{bmatrix}h_{11} & h_{12} & h_{13} & 0 \\h_{21} & h_{22} & h_{23} & 0 \\h_{12}^{*} & {- h_{11}^{*}} & 0 & h_{13}^{*} \\h_{22}^{*} & {- h_{21}^{*}} & 0 & h_{23}^{*}\end{bmatrix}\begin{bmatrix}s_{1} \\s_{2} \\s_{3} \\s_{4}\end{bmatrix}} + \begin{bmatrix}n_{1} \\n_{2} \\n_{3}^{*} \\n_{4}^{*}\end{bmatrix}}$

The channel characteristic matrix defines the various channelcharacteristics between transmitter antennas and receiver antennas,which in this case specifically is two receiver antennas and threetransmit antennas

A decoder for a rate=2 STTD code, for example Code Set-1 in Table 6,generates an estimate of the original transmitted symbols by multiplyingthe received signal by an inverse of the channel matrix as shown in thefollowing equation:

$\begin{bmatrix}{\overset{\sim}{s}}_{1} \\{\overset{\sim}{s}}_{2} \\{\overset{\sim}{s}}_{3} \\{\overset{\sim}{s}}_{4}\end{bmatrix} = {\begin{bmatrix}h_{11} & h_{12} & h_{13} & 0 \\h_{21} & h_{22} & h_{23} & 0 \\h_{12}^{*} & {- h_{11}^{*}} & 0 & h_{13}^{*} \\h_{22}^{*} & {- h_{21}^{*}} & 0 & h_{23}^{*}\end{bmatrix}^{- 1}\begin{bmatrix}r_{1,1} \\r_{1,2} \\r_{2,1}^{*} \\r_{2,2}^{*}\end{bmatrix}}$

Similar decoding methods are performed for Code Set-2 and Code Set-3 todecode all originally encoded information symbols.

The complexity of a matrix inversion operation for a rate=2, threetransmit antenna code is about 33% of that for a rate=2, four transmitantenna code. Since the complexity of the ZF decoder is dominated by itsmatrix inversion operation, the decoding complexity of a rate=2, threetransmit antenna code is about 50% of the decoding complexity of arate=2, four transmit antenna code.

Pilot Pattern for Three Transmit Antenna Transmission

For pilot-assisted channel estimation, known pilot symbols aremultiplexed into the data stream at certain sub-channels (sub-carriers)and certain times. The receiver interpolates the channel informationderived from the pilot symbols and obtains the channel estimates for thedata symbols, and can thereby generate the H matrices referred to above.

A system block diagram is shown in FIG. 11. A MIMO transmitter 10 isshown having four transmit antennas 12,14,16,18. For each transmitantenna, there is a respective OFDM modulator 20,22,24,26. The OFDMmodulators 20,22,24,26 have respective data inputs 26,30,32,34 and pilotinputs 36,38,40,42. It is noted that while one OFDM modulator is shownper antenna, some efficiencies may be realized in combining thesefunctions. Alternatively, since the pilot channel inputs arepredetermined, this can be determined within the OFDM modulators per so.Furthermore, while separate data inputs 28,30,32,34 are shown, these maybe used to transmit data from one or more sources. Encoding may or maynon be performed. Details of the OFDM modulators are not shown. It iswell understood that with OFMD modulation, the data and the pilotchannel symbols are mapped to sub-carriers of an OFDM signal. In orderto generate a particular pilot design, this involves controlling thetiming of when data symbols versus pilot symbols are applied toparticular sub-carriers and for particular OFDM symbol durations.

FIGS. 12 through 23 are examples of pilot designs provided by variousembodiments of the invention. In all of these drawings, time is shown onthe vertical axis and frequency is shown on the horizontal axis. Thesmall circles each represent the content of a particular sub-carriertransmitted at a particular time. A row of such circles represents thesub-carriers of a single OPDM symbol. A vertical column of any of thesedrawings represents the contents transmitted on a given OFDM sub-carrierover time. All of the examples show a finite number of sub-carriers inthe frequency direction. It is to be understood that the number ofsub-carriers in an OFDM symbol is a design parameter and that thedrawings are to be considered to give only one example of a particularsize of OFDM symbol.

FIG. 12 to FIG. 16 show examples of DL pilot patterns for three transmitantennas with a FUSC (fully used sub-channelization) permutation. FUSCis a distributed sub-carrier allocation. In the FUSC permutation, allsub-channels are used and full-channel diversity is employed bydistributing the allocated sub-carriers to sub-channels using aparticular permutation or arrangement.

In FIG. 12, a first block of OFDM symbols on 18 sub-carriers, generallyindicated at 1200, contains pilot and data symbols. The pilots arerepresented by the cross hatched pattern identifying Antenna 1, Antenna2 and Antenna 3. Block 1200 represents a pilot pattern used by the basestation when transmitting to a wireless terminal capable of receivingsignals from all three antennas. In the example of block 1200, pilotsfor a first antenna are located at a first time interval of a secondsub-carrier, a third time interval of a fifth sub-carrier, and a fifthtime interval of an eighth sub-carrier, pilots for a second antenna arelocated at a second time interval of the second sub-carrier, a fourthtime interval of the fifth sub-carrier, and a sixth time interval of theeighth sub-carrier, pilots for a third antenna are a first time intervalof a third sub-carrier, a third time interval of a sixth sub-carrier,and a fifth time interval of a ninth sub-carrier.

A second block of OFDM symbols on nine sub-carriers, generally indicatedat 1210, contains pilot and data symbols. The pilots are represented bythe cross hatched pattern identifying Antenna 1. Block 1210 represents apilot pattern sent by the base station with three antennas for receiptby a wireless terminal that is only capable of receiving a signal from asingle antenna of the three antenna transmitter. As the wirelessterminal is only capable of receiving the signal from one antenna, twopilots are transmitted from the base station to the wireless terminalfor the one antenna. The third pilot typically used when all threeantennas are transmitting is not sent as a pilot to the wirelessterminal as the base station removes it by puncture. Pilots in block1210 are located at the first pair of time intervals of the secondsub-carrier, the third and fourth time intervals of the fifthsub-carrier, and the fifth and sixth time intervals of the eighthsub-carrier. The punctured pilots in close proximity to each of theabove described pairs are located at the first time interval of thethird sub-carrier, the third time intervals of the sixth sub-carrier,and the fifth time intervals of the ninth sub-carrier.

Blocks 1220 and 1230 in FIG. 12 illustrate another set of pilot patternssimilar to 1200 and 1210, respectively, with different pilot locations.

FIGS. 13, 14, 15 and 16 show similar pilot patterns used by basestations for transmitting to wireless terminals capable of receivingfrom all three transmit antennas or from only one of the three antennas.In the example shown in FIG. 16, blocks 1610, 1620, 1630, and 1640 useall three pilot OFDM symbols for one antenna, instead of puncturing oneof the OFDM symbols as in FIGS. 12 to 15.

FIG. 17 shows examples of DL (downlink) pilot patterns for threetransmit antennae with a PUSC (partial usage sub-carrier) Permutation.In the PUSC permutation, sub-channels are divided into multiple portionsthat may then be allocated to different users. As with FUSC above, PUSCemploys full-channel diversity by distributing the allocatedsub-carriers to sub-channels using a particular permutation orarrangement. Blocks 1700, 1710, 1720, 1730, 1740, and 1750 are pilotspatterns transmitted by the base station for three antenna receivecapable wireless terminals and blocks 1760, 1770, 1780, 1785, 1790, and1795 are pilot patterns transmitted by the base station for singleantenna receive capable wireless terminals. Some of the pilot patternsare shown to have nine sub-carriers and some are shown to have 18 overtwo time intervals. More generally, the number of sub-carriers and timeintervals is implementation dependent.

Similarly to DL, uplink (UL) signaling between a base station andwireless terminal involves the transmission of pilots and data. FIGS. 18to 23 show examples of UL pilot patterns in an UL tile format fortransmission to a base station having three transmit antennas.

FIGS. 18 and 19 show examples of UL pilot patterns in UL Tiles for STC.Blocks 1810, 1820, 1830, 1840, 1860, 1870 and 1880 show pilot patternsthat can be transmitted by wireless terminals to the base station. Thepatterns in FIG. 1E show tiles with six OFDM symbols on foursub-carriers and the patterns in FIG. 19 show tiles with three OFDMsymbols on eight sub-carriers. The positions of the pilots in the pilotpatterns ensure that no interference occurs between pilots transmittedfrom different wireless terminals. However, more generally, the numberof sub-carriers is implementation dependent.

In some cases OFDM supports multiple sub-carrier allocation zones with atransmission frame. These zones enable the ability for a communicationsystem to incorporate multiple mobile terminals such that differentsub-carrier allocation zones are allocated for different mobileterminals as desired.

FIGS. 20 and 21 show examples of UL pilot patterns for transmission tothree transmit antennas in a UL Tile for the Optional PUSC Zones.

FIGS. 22 and 23 show examples of UL pilot patterns for transmission tothree transmit antennas in a UL Tile for the Optional AMC (adaptivemodulation and coding) Zones. AMC uses adjacent sub-carriers to formsub-channels.

The number of sub-carriers and OPDM symbols in the pilot patterns ofFIGS. 12 to 23 are only examples and it is to be understood that moregenerally the numbers of sub-carriers and OFDM symbols areimplementation specific.

Space Time Codes with Dynamic Space Time/Frequency Redundancy

There are various sets of known fixed rate codes that can be used forspace time coding of transmissions with multiple transmit antennas. Theknown fixed rate codes have different sizes depending on a number oftransmit symbols to be transmitted within a code block. A block isreferred to generally as a time index with multiple time intervals,however it is to be understood that the block may alternatively be afrequency index with multiple frequencies. One code, identifiedhereafter as G1, transmits one transmit symbol in one block that iscapable of being transmitted on one antenna, for example [s₁].Therefore, for a single antenna one G1 code results in a rate==code, fora two transmit antenna, two G1 codes can be transmitted, one on eachantenna, which result in a rate=2 code, and for a three transmit antennathree G1 codes can be transmitted, one on each antenna for a rate=3code. Another code, identified hereafter as G2, transmits two transmitsymbols in two blocks that are transmitted on two antennas, for examplean Alamouti code such as

$\begin{bmatrix}s_{1} & s_{2} \\{- s_{2}^{*}} & s_{1}^{*}\end{bmatrix}.$

Therefore, for a two transmit antenna one G2 code results in a rate=1code. A further code, identified hereafter as G3, transmits threetransmit symbols in two blocks that are transmitted on three antennas,for example

$\quad{\begin{bmatrix}s_{1} & s_{2} & s_{3}^{*} \\{- s_{2}^{*}} & s_{1}^{*} & s_{3}^{*}\end{bmatrix}.}$

Therefore, for a three transmit antenna one G3 code results in arate=3/2 code. For two transmit antennas it is possible to transmitusing codes G1 or G2, for three transmit antennas it is possible totransmit using codes G1, G2 and G3, for four transmit antennas it ispossible to transmit using codes G1, G2, G3 and G4, and so on.

According to an embodiment of the present invention the codes arecombined in both space and time to construct space-time codes whichresult in a mix of spatial multiplexing and transmit diversity. Thisprovides a layer based dynamic space-time/frequency redundancy. Thecodes can be used to support users of different needs, such asthroughput and reliability.

FIGS. 24A-24H illustrate examples of two transmit antenna codes usingthe fixed rate codes identified above as G1 and G2. The codes are shownfor various block lengths, L=3 to 5, where the block length correspondsto the number of blocks along the vertical axis indicated as a timeindex. More generally, as described above the vertical axis couldrepresent a frequency index. The antenna index is indicated along thehorizontal axis and indicates the number of transmit antenna. In thevariable rate code examples of FIGS. 24A-24H the number of antennas istwo.

For a block length equal to three, FIG. 24A shows a code with a coderate equal to 4/3, generally indicated at 2410, and includes a single G2code 2410 in a first portion of the three block space and two G1 codes2420 in a second portion of three block space.

Another case in which the block length is equal to three is shown inFIG. 24B. A different code with a code rate equal to 2, generallyindicated at 2430, includes six G1 codes 2420, spread within the entirethree block space.

For a block length equal to four, FIG. 24C shows a code with a code rateequal to 1, generally indicated at 2440, and includes two G2 codes 2410,one in a first portion of the three block space and one in a secondportion of the three block space.

Another case in which the block length is equal to four is shown in FIG.24D. A different code with a code rate equal to 3/2, generally indicatedat 2450, includes one G2 code 2410 in a first portion of the four blockspace and four G1 codes 2420 spread within a second portion of the fourblock space.

Yet another case in which the block length is equal to four is shown inFIG. 24E. A different code with a code rate equal to 2, generallyindicated at 2460, includes eight G1 codes 2420, spread within theentire four block space.

For a block length equal to five, FIG. 24P shows a code with a code rateequal to 6/5, generally indicated at 2470, and includes two G2 codes2410 in a first portion of the five block space and two G1 codes 2420 ina second portion of the five block space.

Another case in which the block length is equal to five is shown in FIG.24G. A different code with a code rate equal to 8/5, generally indicatedat 2480, includes one G2 code 2410 in a first portion of the four blockspace and six G1 codes 2420 spread within a second portion of the fiveblock space.

Yet another case in which the block length is equal to five is shown inFIG. 24H. A different code with a code rate equal to 2, generallyindicated at 2490, includes ten G1 codes 2420, spread within the entirefive block space.

FIGS. 25A-25E illustrate several examples of arrangements of codesidentified above as G1, G2 and G3 to be used for three transmitantennas. The code rates for codes in FIGS. 25A-25E are 5/2, 2, 3, 9/4and 3/2, respectively.

The examples shown in FIGS. 24 and 25 are but a few of the arrangementspossible for obtaining particular variable code rate codes. In FIG. 24A,the rate=4/3 code 2400 shown for the block length equal to three has aG2 code 2410 followed by two G1 codes 2430 in the incremented time indexdirection. An alternative to this may be the two G1 codes 2420 firstfollowed by the G2 code 2410 in the incremented time index direction.Similar rearrangements of other illustrated examples are possible and tobe considered within the scope of the invention for the respectivespace-time/frequency codes.

Table 9 includes a list of code rates for corresponding block lengths ina 2 transmit antenna. The two transmit antenna variable rate STC codesshown in FIGS. 24A-24H are possible arrangements associated with thecode rates represented in Table 9 for block lengths (L) equal to 2, 3, 4and 5.

TABLE 9 2-Transmit-Antenna Code Set and Coding Rate Block Length (L)Code Rates (R) 2 1.00 2.00 3 1.33 2.00 4 1.00 1.5  2.00 5 1.20 1.6  2.006 1.00 1.33 1.67 2.00 7 1.14 1.43 1.71 2.00 8 1.00 1.25 1.50 1.75 2.00 91.11 1.33 1.56 1.78 2.00 10 1.00 1.20 1.40 1.60 1.80 2.00 11 1.09 1.271.45 1.64 1.82 2.00 12 1.00 1.17 1.33 1.50 1.67 1.83 2.00 13 1.08 1.231.38 1.54 1.69 1.85 2.00 14 1.00 1.14 1.29 1.43 1.57 1.71 1.86 2.00 151.07 1.20 1.33 1.47 1.60 1.73 1.87 2.00

Table 9 is an example of resulting code rates for different blocklengths in a 2 transmit antenna. Other multi transmit antennas havetheir own respective code rates that could be similarly tabulated fordifferent block lengths.

In some embodiments the codes are used for transmission of symbols onindividual sub-carriers. Code Set-1 in Table 6 is an example of thefirst two blocks of FIG. 25A. The G2 code is represented by

$\quad\begin{bmatrix}s_{1} & s_{2} \\{- s_{2}^{*}} & s_{1}^{*}\end{bmatrix}$

and the two G1 codes beside the G2 code are represented by [s₃] and[s₄*]. Additional time intervals t+2t and t+3T would be required inaddition to Table 6 to fully represent the additional two blockscontaining the remaining six G1 codes.

Numerous modifications and variations of the present invention arepossible in light of the above teachings. It is therefore to beunderstood that within the scope of the appended claims, the inventionmay be practised otherwise than as specifically described herein.

1-41. (canceled)
 42. A method for transmitting on four antennascomprising: pre-coding information bits to generate four transmitsymbols; encoding two of the transmit symbols into a first matrix andencoding another two of the transmit symbols into a second matrix;transmitting the two matrices on four antennas over four time intervalsor four frequencies by: transmitting the first matrix on two antennasduring two of the four time intervals or at two of the four frequencies;transmitting the second matrix on the other two antennas during theother two of the four time intervals or at the other two of the fourfrequencies; wherein the pre-coding and encoding are such that all ofthe information bits are represented in what is transmitted from each ofthe four antennas.
 43. The method of claim 42, wherein the pre-codingcomprises: generating the four transmit symbols by mapping M informationbits as two sets of M/2 bits, wherein the first set of M/2 bits ismapped on a first and a third mapping constellation to produce first andthird transmit symbols, and the second set of M/2 bits is mapped on asecond and a fourth mapping constellation to produce second and fourthtransmit symbols.
 44. The method of claim 43, wherein the first andsecond transmit symbols are encoded in the first matrix and the thirdand fourth transmit symbols are encoded in the second matrix.
 45. Themethod of claim 43, wherein the second and fourth mapping constellationsare the same as the first and third mapping constellations,respectively.
 46. The method of claim 42, wherein the transmitting thetwo matrices over the four time intervals comprises transmitting in adiversity order.
 47. The method of claim 42, wherein the two matricesare located within a space time block code (“STBC”).
 48. The method ofclaim 47, wherein remaining positions of the STBC are set to null.
 49. Aprocessor configured to: pre-code information bits to generate fourtransmit symbols; encode two of the transmit symbols into a first matrixencode another two of the transmit symbols into a second matrix;transmit the two matrices on four antennas over four time intervals orfour frequencies by: transmitting the first matrix on two antennasduring two of the four time intervals or at two of the four frequencies;transmitting the second matrix on the other two antennas during theother two of the four time intervals or at the other two of the fourfrequencies; wherein the pre-code and encode occur such that all of theinformation bits are represented in what is transmitted from each of thefour antennas.
 50. The processor of claim 49, wherein the pre-codingcomprises the processor: generating the four transmit symbols by mappingM information bits as two sets of M/2 bits, wherein the first set of M/2bits is mapped on a first and a third mapping constellation to producefirst and third transmit symbols, and the second set of M/2 bits ismapped on a second and a fourth mapping constellation to produce secondand fourth transmit symbols.
 51. The processor of claim 50, wherein thefirst and second transmit symbols are encoded in the first matrix andthe third and fourth transmit symbols are encoded in the second matrix.52. The processor of claim 50, wherein the second and fourth mappingconstellations are the same as the first and third mappingconstellations, respectively.
 53. The processor of claim 49, wherein thetransmitting the two matrices over the four time intervals comprises theprocessing hardware being configured to transmit in a diversity order.54. The processor of claim 49, wherein the two matrices are locatedwithin a space time block code (“STBC”).
 55. The processor of claim 54,wherein remaining positions of the STBC are set to null.
 56. A device,comprising: four antennas; communication circuitry; and processinghardware coupled to the four antennas and the communication circuitry,wherein the processing hardware is configured to operate with the fourantennas and the communication circuitry to: pre-code information bitsto generate four transmit symbols; encode two of the transmit symbolsinto a first matrix and encode another two of the transmit symbols intoa second matrix; transmit the two matrices on the four antennas overfour time intervals or four frequencies by: transmitting the firstmatrix on two antennas during two of the four time intervals or at twoof the four frequencies; transmitting the second matrix on the other twoantennas during the other two of the four time intervals or at the othertwo of the four frequencies; wherein the pre-code and encode occur suchthat all of the information bits are represented in what is transmittedfrom each of the four antennas.
 57. The device of claim 56, wherein thepre-coding comprises the processing hardware being configured to:generate the four transmit symbols by mapping M information bits as twosets of M/2 bits, wherein the first set of M/2 bits is mapped on a firstand a third mapping constellation to produce first and third transmitsymbols, and the second set of M/2 bits is mapped on a second and afourth mapping constellation to produce second and fourth transmitsymbols.
 58. The device of claim 57, wherein the first and secondtransmit symbols are encoded in the first matrix and the third andfourth transmit symbols are encoded in the second matrix.
 59. The deviceof claim 57, wherein the second and fourth mapping constellations arethe same as the first and third mapping constellations, respectively.60. The device of claim 56, wherein the two matrices are located withina space time block code (“STBC”).
 61. The device of claim 60, whereinremaining positions of the STBC are set to null.